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Singular (software)
Singular (typeset Singular) is a computer algebra system for polynomial computations with special emphasis on the needs of commutative algebra, commutative and non-commutative algebra, algebraic geometry, and singularity theory. Singular has been released under the terms of GNU General Public License. Problems in non-commutative algebra can be tackled with the Singular offspring Plural. Singular is developed under the direction of Wolfram Decker, :de:Gert-Martin Greuel, Gert-Martin Greuel, :de:Gerhard Pfister (Mathematiker), Gerhard Pfister, and Hans Schönemann, who head Singular's core development team within the Department of Mathematics of the University of Kaiserslautern, Technische Universität Kaiserslautern. In the Deutsche Forschungsgemeinschaft, DFG Priority Program 1489, interfaces to GAP computer algebra system, GAP, Polymake and Gfan are being developed in order to cover recently established areas of mathematics involving convex geometry, convex and algebraic geometry, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Kaiserslautern
Technical University of Kaiserslautern (German: ''Technische Universität Kaiserslautern'', also known as TU Kaiserslautern or TUK) is a public university, public research university in Kaiserslautern, Germany. There are numerous institutes around the university, including two Fraunhofer Institutes (IESE and ITWM), the Max Planck Institute for Software Systems (MPI SWS), the German Research Centre for Artificial Intelligence, German Research Center for Artificial Intelligence (DFKI), the Institute for Composite Materials (IVW) and the Institute for Surface and Thin Film Analysis (IFOS), all of which cooperate closely with the university. TU Kaiserslautern is organized into 12 faculties. Approximately 14,869 students are enrolled at the moment. The TU Kaiserslautern is part of the Software-Cluster along with the Technische Universität Darmstadt, the Karlsruhe Institute of Technology and Saarland University. The Software-Cluster won the German government's ''Spitzencluster'' comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System Software For MacOS
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Algebra System Software For Linux
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Of Computer Algebra Systems
The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language. A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorithms, efficient data structures and a fast kernel. General These computer algebra systems are sometimes combined with "front end" programs that provide a better user interface, such as the general-purpose GNU TeXmacs. Functionality Below is a summary of significantly developed ''symbolic'' functionality in each of the systems. via SymPy via qepcad optional package Those which do not "edit equations" may have a GUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tropical Geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: : x \oplus y = \min\, : x \otimes y = x + y. So for example, the classical polynomial x^3 + 2xy + y^4 would become \min\. Such polynomials and their solutions have important applications in optimization problems, for example the problem of optimizing departure times for a network of trains. Tropical geometry is a variant of algebraic geometry in which polynomial graphs resemble piecewise linear meshes, and in which numbers belong to the tropical semiring instead of a field. Because classical and tropical geometry are closely related, results and methods can be converted between them. Algebraic varieties can be mapped to a tropical counterpart and, since this process still retains some geometric information about the original variety, it can be used to help prove and generalize classica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toric Geometry
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Some authors also require it to be normal. Toric varieties form an important and rich class of examples in algebraic geometry, which often provide a testing ground for theorems. The geometry of a toric variety is fully determined by the combinatorics of its associated fan, which often makes computations far more tractable. For a certain special, but still quite general class of toric varieties, this information is also encoded in a polytope, which creates a powerful connection of the subject with convex geometry. Familiar examples of toric varieties are affine space, projective spaces, products of projective spaces and bundles over projective space. Toric varieties from tori The original motivation to study toric varieties was to study torus embeddings. Given the algebraic t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Geometry
In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, game theory, etc. Classification According to the Mathematics Subject Classification MSC2010, the mathematical discipline ''Convex and Discrete Geometry'' includes three major branches: * general convexity * polytopes and polyhedra * discrete geometry (though only portions of the latter two are included in convex geometry). General convexity is further subdivided as follows: *axiomatic and generalized convexity *convex sets without dimension restrictions *convex sets in topological vector spaces *convex sets in 2 dimensions (including convex curves) *convex sets in 3 dimensions (including convex surfaces) *convex sets in ''n'' dimensions (including convex hy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymake
polymake is software for the algorithmic treatment of convex polyhedra. Albeit primarily a tool to study the combinatorics and the geometry of convex polytopes and polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs, tropical objects, toric varieties and other objects. In particular, its capability to compute the convex hull and lattice points of a polytope proved itself to be of quiet use for different kinds of research. polymake has been cited in over 300 recent articles indexed by Zentralblatt MATH as can be seen from its entry in the swMATH database. Special features and applications polymake exhibits a few particularities, making it special to work with. Firstly, polymake can be used within a Perl script. Moreover, users can extend polymake and define new objects, properties, rules for computing properties, and algorithms. Secondly, it exhibits an internal client-server scheme to accommodate the usage of Perl for o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GAP Computer Algebra System
GAP (Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory. History GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westfälische Technische Hochschule Aachen, Germany from 1986 to 1997. After the retirement of Joachim Neubüser from the chair of LDFM, the development and maintenance of GAP was coordinated by the School of Mathematical and Computational Sciences at the University of St Andrews, Scotland. In the summer of 2005 coordination was transferred to an equal partnership of four 'GAP Centres', located at the University of St Andrews, RWTH Aachen, Technische Universität Braunschweig, and Colorado State University at Fort Collins; in April 2020, a fifth GAP Centre located at the TU Kaiserslautern was added. Distribution GAP and its sources, including packages (sets of user contributed programs), data library (including a list of small groups) and the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deutsche Forschungsgemeinschaft
The German Research Foundation (german: Deutsche Forschungsgemeinschaft ; DFG ) is a German research funding organization, which functions as a self-governing institution for the promotion of science and research in the Federal Republic of Germany. In 2019, the DFG had a funding budget of €3.3 billion. Function The DFG supports research in science, engineering, and the humanities through a variety of grant programmes, research prizes, and by funding infrastructure. The self-governed organization is based in Bonn and financed by the German states and the federal government of Germany. As of 2017, the organization consists of approximately 100 research universities and other research institutions. The DFG endows various research prizes, including the Leibniz Prize. The Polish-German science award Copernicus Award, Copernicus is offered jointly with the Foundation for Polish Science. According to a 2017 article in ''The Guardian'', the DFG has announced it will publish its re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
